probability with coins

[eddy2017]

A teacher was explaining this probability problem. Everything made perfect sense until he said something. I couldn't follow.
I would like you to help me reason the why of that operatin he did there. I have written all the steps he took and got up to the point where I did not understand.
Deep thanks for help and support.
eddy

In a jar, there are half as many nickles as there are pennies, twice as many dimes as there are nickels, and 3 times as many dimes as there are quarters. There are 12 pennies in the jar. If the first two randomly selected coins from the jar are both pennies and they are not replaced, what is the probability that the next randomly selected coin is a quarter?


We’re talking about coins here and the probability that we select quarters.

Remember that the way we find probability is dividing what we want by the number of possibilities we have. (Favorable outcomes/total of outcomes)

P =The results we want

number of possibilities



we have 12 pennies in the jar

we have half as many nickels as there are pennies= half of 12=6 nickels

twice as many dimes as there are nickles = 2*6 =12 dimes

up to here i understand everything. The following step is the one is am not making sense out of. once we have the amount of quarter is very easy to solve the problem.

and 3 times as many dimes as there are quarters?

The teacher who solved this, said that we could not multiply 12 * 3, but instead we needed to perfom division. He said
12 dimes is just three times the amount of quarters so

But we have to divide 12/3=4

And then we have 4 quarters.

I don’t understand the logic behind the division in this step. Up to this point, he multiplied everything and here he divided. Why?.
My guess: Because we don't know the quarters so we need to divide 12 dimes(what we know)

 

[lev888]

No, it's not because "we don't know the quarters". The fact that we don't know something does not tell us how to find it.
You need to carefully read the problem statement:
"3 times as many dimes as there are quarters."
What does it tell you?

 

[eddy2017]

No, it's not because "we don't know the quarters". The fact that we don't know something does not tell us how to find it.
You need to carefully read the problem statement:
"3 times as many dimes as there are quarters."
What does it tell you?

Twice as many dimes as there are nickles = 2*6 =12 dimes ( but here I know how many nickels I have, so it is easy!), but here,

3 times as many dimes as there are quarters. ( I don't know the quarters!).
there are 12 dimes (this I know).
? . Any hint. I do not really know.
I would have done this: 3(12), but I know it is wrong, but why?.
Thanks.

 

[lev888]

Twice as many dimes as there are nickles = 2*6 =12 dimes ( but here I know how many nickels I have, so it is easy!), but here,

3 times as many dimes as there are quarters. ( I don't know the quarters!).
there are 12 nickels (this I know).
? . Any hint. I do not really know.
I would have done this: 3(12), but I know it is wrong, but why?.
Thanks.

You now know how many dimes there are: 12. We also know that there are "3 times as many dimes as there are quarters". What does this tell you about the number of quarters?

 

[eddy2017]

You now know how many dimes there are: 12. We also know that there are "3 times as many dimes as there are quarters". What does this tell you about the number of quarters?

Sorry, I wrote nickels instead of dimes @#3. I rectified it.
What does this tell you about the number of quarters?

Wait, let me think.

 

[eddy2017]

Sorry, I wrote nickels instead of dimes @#3. I rectified it.
What does this tell you about the number of quarters?

Wait, let me think.

Holy Lee, I think I have it.
It tells me that I have to have only 4 quarters because if the dimes are 12, and there are 3 times as many dimes as quarters, then, the quarters have to be 4 ,because 4*3(times as many) equals 12 (the amount of dimes).

 

[HallsofIvy]

Holy Lee

A southern boy!

 

[eddy2017]

. Yes, sir. a redneck trying to understand Math, not a pretty pic.